The following is not a question: Can something come from nothing?

[Angrboda]

Your definition of entropy and the arrow of time seems circular. Water falls because there are more possible states it can be after than before, yet this is just the definition of the arrow of time itself, so you haven't really explained the arrow of time, simply shown something that occurs if you assume a specific arrow of time. (Which may be violated, e.g. fluctuation theorem and time-reversal interpretation of QM.)

The arrow of time is a result by entropy itself. The laws of physics are time-independent, which is why we can "retrodict" things with the laws of physics. What we call "past" and "future" are simply a result of a recognition of the difference between 2 states of affairs wherein one state has less entropy than another. The reason for this is because is is the case that there are more ways to be in a disordered state than an ordered state. There's no circularity there.

The problem is explaining why entropy should increase rather than decrease. By using the terms 'increase' and 'decrease' with regard to entropy, you're already appealing to a concept of time that has a direction, thus the circularity.